Let F(x)={1+cx−1x,x≠0,2,x=0.F(x)= \begin{cases} \dfrac{\sqrt{1+cx}-1}{x}, & x\neq0,\\[4pt] 2, & x=0. \end{cases}…

Mathematics

Problem

Let F(x)={1+cx−1x,x≠0,2,x=0.F(x)= \begin{cases} \dfrac{\sqrt{1+cx}-1}{x}, & x\neq0,\\[4pt] 2, & x=0. \end{cases} Find the value of the constant cc so that FF is continuous at x=0x=0. a) c=2c=2 b) c=1c=1 c) c=4c=4 d) c=6c=6

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